Question

A rectangular prism has a base length of 6 units, base width of 5 units, and height of 4 units. The bases are shaded. The lateral area is . The area of the two bases together is . The total surface area is

Answer 1

1) 88.0 units^2

2) 60.0 units^2

3) 148.0 units^2

Explanation:

1)

The lateral area of a rectangular prism is equal to the sum of the areas of the 4 lateral faces.

Since the areas of 2 opposite faces are equal, the lateral area is:

$A_L=2A_1 + 2A_2$

where $A_1,A_2,A_3$ are the areas of the two faces.

Here we have:

L = 6 is the length of the base

w = 5 is the width of the base

h = 4 is the height of the prism

So we have:

$A_1=L\cdot h = (6)(4)=24$

$A_2=w\cdot h =(5)(4)=20$

So the lateral surface area is

$A_L = 2(24)+2(20)=88$

2)

The area of one base of the prism is the product of the length of the base and the width:

$A=L\cdot w$

Where here we have

L = 6 is the length of the base

w = 5 is the width of the base

So the area of 1 base is

$A=(6)(5)=30$

And here we have 2 bases, therefore the area of the two bases together is twice the area of the single base:

$A_b=2A=2(30)=60$

3)

The total surface area of the prism is given by the sum of the area of the two bases + the lateral area of the prism:

$A=A_b+A_L$

where

$A_b$ is the area of the bases

$A_L$ is the lateral area

Here for this prism we have:

$A_b=60$ (area of the bases)

$A_L=88$ (lateral area)

So the total surface area is

$A=60+88=148$

Answer 2

Answer:

88 units squared

60 units squared

148 units squared